Question

20. Find the inverse of each function. Then graph the function and its inverse.

A. g(x)=2r-1
B. f(x)=2+2
-2
+9(x)
-2
O
-2
2
4x
-4
-2
-2
O
-2
y
2
4 x

Answer 1

The graph of each function and the inverse is attached

How to find the inverse of the function

The inverse of the function is calculated by making x the subject of formula and interchanging the variables. This is done as as follows

A. g(x) = 2x-1

let y = g(x)

y = 2x - 1

2x = y + 1

x = (y + 1) / 2

interchanging the variables

y = (x + 1) / 2.

The inverse of g(x) = 2x-1 is g⁻¹(x) = (x + 1) / 2.

B. f(x) = 2/3 x + 2

let y = f(x)

y = 2/3 x + 2

(y - 2) = 2/3 x

x = 3/2 (y - 2)

interchanging the variables

y = 3/2 (x - 2)

The inverse of f(x) = 2/3 x + 2 is f⁻¹(x) = 3/2 (x - 2)